A Class of Steffensen-Type Iterative Methods for Nonlinear Systems

A class of iterative methods without restriction on the computation of Frechet derivatives including multisteps for solving systems of nonlinear equations is presented. By considering a frozen Jacobian, we provide a class of m-step methods with order of convergence . A new method named as Steffensen-Schulz scheme is also contributed. Numerical tests and comparisons with the existing methods are included.

[1]  Jafar Saberi-Nadjafi,et al.  A Hybrid of the Newton-GMRES and Electromagnetic Meta-Heuristic Methods for Solving Systems of Nonlinear Equations , 2009, J. Math. Model. Algorithms.

[2]  Mohammad Taghi Darvishi,et al.  HIGH-ORDER NEWTON-KRYLOV METHODS TO SOLVE SYSTEMS OF NONLINEAR EQUATIONS , 2011 .

[3]  J. Traub.  Iterative Methods for the Solution of Equations , 1982 .

[4]  Fazlollah Soleymani,et al.  NOVEL COMPUTATIONAL DERIVATIVE-FREE METHODS FOR SIMPLE ROOTS , 2012 .

[5]  Z. Bai,et al.  A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations , 2007 .

[6]  F Soleymani.  ON A NOVEL OPTIMAL QUARTICALLY CLASS OF METHODS , 2011 .

[7]  Homer F. Walker,et al.  Globally Convergent Inexact Newton Methods , 1994, SIAM J. Optim..

[8]  Sergio Amat,et al.  On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods , 2011, J. Comput. Appl. Math..

[9]  Alicia Cordero,et al.  A modified Newton-Jarratt’s composition , 2010, Numerical Algorithms.

[10]  Peng Zhao,et al.  A family of fourth-order Steffensen-type methods with the applications on solving nonlinear ODEs , 2011, Appl. Math. Comput..

[11]  Ying Zhang,et al.  Finding the Roots of System of Nonlinear Equations by a Novel Filled Function Method , 2011 .

[12]  Predrag S. Stanimirović,et al.  A Higher Order Iterative Method for Computing the Drazin Inverse , 2013, TheScientificWorldJournal.

[13]  Fayyaz Ahmad,et al.  An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs , 2013, J. Appl. Math..

[14]  Alicia Cordero,et al.  Basins of Attraction for Various Steffensen-Type Methods , 2014, J. Appl. Math..